1
MA 15200
Lesson 26
Section 2.7
This lesson is on
inverse functions
.
Examine the temperature formulas below.
32
5
9
)
32
(
9
5
C
F
F
C
Replace F in the first equation with 50º.
10
)
18
(
9
5
)
32
50
(
9
5
C
C
C
Now, replace C in the second with 10º.
50
32
18
32
)
10
(
5
9
F
F
F
Notice these functions do opposite things.
The first equation turned 50°F to 10°C.
The
second equation turned 10°C back to 50°F.
Such functions are called inverse functions.
Here are two other functions that are inverses of each other.
3
23
2
x
y
x
and y
Notice that in the first function a number is multiplied by 2, then 3 is added to the result.
In the second function 3 is subtracted from a number, then divided by 2.
Begin with 5 as
the number in the first function. Multiply by 2, and then add 3; the result is 13.
Now, let
13 be the number in the second function.
Subtract 3, divide by 2; the result is 5 (the
original number selected for the first function).
Let the first equation above be
3
( )
2
3 and the second be
( )
2
x
f x
x
g x
.
Examine:
33
( ( ))
2
3
3 3
22
2
3 3
2
( ( ))
(2
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 Fall '09
 Inverse Functions, Formulas, Inverse function

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